Product of delta exponentials with fixed t and s

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Theorem: Let $\mathbb{T}$ be a time scale, $t,s \in \mathbb{T}$, and let $p,q \in \mathcal{R}\left(\mathbb{T},\mathbb{C}\right)$ be regressive functions. The following formula holds: $$e_p(t,s;\mathbb{T})e_q(t,s;\mathbb{T})=e_{p \oplus q}(t,s;\mathbb{T}),$$ where $e_p$ denotes the delta exponential and $\oplus$ denotes circle plus.

Proof: